For "it's your turn" Georges suggests ordo te vocat or nunc sunt tuae partes (the latter particularly for when it's someone's turn to perform some duty). The only usage of the former I can find is in the Saturnalia of Macrobius, 2,2,12, where a group of people are telling each other more or less lewd jokes, and then...
Inter haec cum Servius ordine se vocante per verecundiam sileret: Omnes nos, inquit Evangelus, inpudentes grammatice pronuntias, si tacere talia vis videri tuitionem pudoris
While they were talking so, when Servius, when it was his turn, remained silent due to his propriety, Evangelus said: You declare us all shameless, you grammarian, if you would that passing over such things in silence looks like a defence of your shame.
The latter is Ciceronian. Georges gives the example: si suae partes essent hospitum recipiendorum, which is an (inexplicably) modified quote from the Verrine orations, II.1:
ostendit munus illud suum non esse; se, cum suae partes essent hospitum recipiendorum, tum ipsos tamen praetores et consules, non legatorum adseculas, recipere solere
he said that that was not his job; when it was his turn to host guests, he said, he was used to host praetors and consuls themselves, not legates' attendants
Very good in terms of pedigree; still, for your example, "wait your turn," this idea of it being one's "shift," so to speak, to do a certain duty, seems less apt. Using therefore the ordo expression, we get:
Exspecta, quoad ordo te vocet.